Optical low-pass spatial filters

ABSTRACT

AN OPTICAL LOW-PASS SPATIAL FILTER FOR LOW PASS SPATIALLY FILTERING PHOTOGRAPHIC IMAGERY INFORMATION. THE LOW-PASS SPATIAL FILTER INCLUDES A SOURCE OF DIFFUSED ILLUMINATION, A MASK DISPOSED IN FRONT OF THE SOURCE OF DIFFUSED ILLUMINATION AND HAVING A CIRCULARY-SYMMETRIC TRANSMISSIVITY PATTERN, AND A LENS SPACED IN FRONT OF THE MASK A DISTANCE EQUAL TO THE FOCAL LENGTH OF THE LENS FOR REFRACTING ILLUMINATION DIRECTED THEREON FROM THE SOURCE OF ILLUMINATION AFTER PASSAGE THROUGH THE MASK.

June 20, 1972 s. BIERNsoN ETAL 3,671,101

OPTICAL LOW-PASS SPATIAL FILTER Original Filed Oct. 29, 1968 2Sheets-Sheet 1 .2.5mm mozmacmw z. W

....:iiiiiia a mmtwoa L .359066522 2f 35.32 Sm @2255...

Bm Stw NE wozmaaww z. NE

June 20, 1972 G, BIERNSON ETAL 3,671,107

OPTICAL LOW-PASS SPATIAL FILTER Original Filed Oct. 29, 1968 2Sheets-Sheet 2 DIFFUSE RADIATOR SPATIAL FILTER MASK L LENS 23 MIZZZZZZZZZZZZZZZZZI POSITIVE BLURRED NEGATIVE FIG. 2

3,671,107 OPTICAL LOW-PASS SPATIAL FILTERS George Biernson, Concord,Raymond Euling, Sudbury,

and Paul W. Jones, Franklin, Mass., assignors to Sylvania ElectricProducts Inc.

Original application Oct. 29, 1968, Ser. No. 771,585, now Patent No.3,615,433. Divided and this application Oct. 5, 1970, Ser. No. 78,266

Int. Cl. G02b 27/00 U.S. Cl. 350-162 SF 1 Claim ABSTRACT OF THEDISCLOSURE CROSS-REFERENOE TO RELATED APPLICATION This application is adivision of application Ser. No. 771,585, filed Oct. 29, 1968, 110W PatN0. 3,615,433 and assigned to the assignee of the present application.

BACKGROUND OF THE INVENTION The present invention relates to imageryprocessing and, more particularly, to a feedback image enhancementprocess for enhancing the details of photographic images.

High-quality photographic film is available that can record clearlyphotographic negative images over a range of light intensities of aboutl000z1. Such a high range of light intensities is needed forphotographing high-contrast outdoor scenes in order to record detaileffectively both in brightly-lighted areas and in dimly-lighted areas.For effective viewing, it is usually desirable to derive positive paperprints from negatives of such scenes. However, the range of lightintensities that can be recorded clearly on photographic printing paperis quite low, often not much greater than :1, and so a great deal ofimagery detail in a negative of a high-contrast scene can be lost inmaking a positive print therefrom. To avoid this loss of imagery detail,the range of the imagery data recorded on the photographic negative isoften compressed so that it can be conveyed effectively on aphotographic medium of low dynamic range. This compression of the rangeof the imagery data is referred to herein as image enhancement.

The basic philosophy underlying image enhancement is that byilluminating the dark areas of a negative strongly, and the light areasweakly, the operating range of illumination applied to expose a positivecan be made to be much lower than the range of transmissivity values ofthe negative. Ideally, the illumination is varied gradually over thenegative in order that the pattern of the i1- lumination does not itselfcontribute artificial detail to the image recorded on the positive.Thus, the positive records an enhanced image of relatively low operatingrange. The same image enhancement effect can also be achieved by placinga medium of non-uniform transmissivity between the negative and a Ifilmand uniformly i1- luminating the negative to expose the film through themedium of non-uniform transmissivity. The medium of non-uniformtransmissivity operates to attenuate weakly the light from the darkareas of the negative and to at- United States PatentO ,Y 3,611,107Patented June 20, 1972 ICC tenuate greatly the light from the lightareas of the negative.

The approximate elect of the above-described image enhancement, whetherusing varying amounts of illumination or a medium of non-uniformtransmissivity, is to compensate to a large extent for variations ofillumination on the original scene. Consequently, the enhanced imagerecorded on the positive is similar to what would be recorded withoutimage enhancement if the illumination on the original scene were muchmore uniform.

Various conventional prior art methods and apparatus have been employedheretofore for enhancing photographic images to compress the range ofthe photographic data contained in a negative or a positive. Twomethods, one photographic in nature and the other electro-optical innature, have been Widely .used to implement image enhancement. Each ofthese methods can be employed to produce an enhanced positive from anoriginal negative, or to produce an enhanced negative from an originalpositive. For simplicity, the following discussion will consider onlythe former alternative; however, the latter alternative is essentiallythe same.

In the photographic method of image enhancement, a negative of a sceneis uniformly illuminated and the image impressed thereon is blurred bysuitable photographic apparatus. An unexposed film spaced from thenegative is exposed with the blurred image and then developed to form ablurred positive, the blurred positive being designated a mask. The maskis characteristically dank in the regions where the original negative islight, and light in the regions where the original negative is dark. Themask is then superimposed on the original negative, and themask-negative combination is uniformly illuminated. The combined imagesof the mask and the original negative are then focused onto an unexposedfilm spaced from the mask-negative combination, which film is exposedwith the images and then developed to represent the desired enhancedpositive. Since the above-described mask is dark in the regions wherethe original negative is light, and vice versa, the range of lightintensities focused onto the second positive, i.e., the enhancedpositive, can be much lower than the range of transmissivity values ofthe enhanced positive. In other words, the range of imagery data iscompressed. Moreover, since the image on the mask is blurred, it doesnot add very much imagery detail to the enhanced positive.

The blurred positive in the above-described photographic method is oftenformed by using suitable photographic apparatus to expose a defocusedimage of the negative on the iilm used to form the positive mask. Theprimary effect of defocusing the image on the negative is to attenuatethe high spatial-frequency components of the image, and thereby to blurthe sharp lines of demarcation between the light and dark areas of theimage. Therefore, the blurring operation represents a low-pass spatialiltering. There are many other ways that this low-pass spatial filteringof the image can be implemented which have different effects on how thecomponents of the image are modified. However, these differences do notalter the basic principle of image enhancement.

As a variation of the above-described method for deriving an enhancedpositive, a mask is obtained as in the above-described method (byexposing and developing a lm with a blurred negative image), theoriginal negative is spaced from the mask, and the mask illuminated sothat the illumination falling on the negative is a defocused (orblurred) image of the mask. The image of the illuminated negative isthen forcused onto lm to expose an enhanced positive. The aboveoperation provides two stages of low-pass spatial filtering, the rststage of lowpass spatial filtering operating between the negative andthe mask, and the second stage then operating between the mask and thenegative.

In the electro-optical prior art method of photographic imageenhancement, an original negative of a scene is scanned with a broadbeam of light from a cathode ray tube. The cathode ray tube iscontrolled so as to have a scan rate which is varied in accordance withthe amount of light energy that passes through the negative. Typically,the beam used to scan the negative is made much broader than the imagedetail on the negative but much narrower than the negative itself. Thenegative is scanned with the light beam and the light energy passingthrough the negative is sampled by a photo-detector to controlappropriately the scan rate of the cathode ray tube. More particularly,the scan rate of the cathode ray tube is controlled such that thegreater the amount of light energy measured by the photo-detector, thefaster is the scan rate. The variations in light energy therefore causethe beam to scan rapidly over the low-density areas (light areas) of thenegative and slowly over the high-density areas (dark areas). Theilluminated image produced by scanning the negative with the light beamis focused onto suitable unexposed film, which is exposed by the imageand then developed to form the enhanced positive.

Although the electro-optical method of image enhancement is implementedin quite a different manner from the basic photographic method describedabove, the two methods are mathematically equivalent. More specifically,it can be demonstrated that the same pattern of light energy applied tothe negative by the cathode ray tube can be achieved by the photographicmethod if two stages of low-pass spatial filtering are employed asdescribed hereinabove, that is, between the negative and the mask andthen between the mask and the negative.

The image enhancement techniques and methods desiribed above are fairlyeffective in compressing the range of imagery data in many photographicsituations. However, they have rather severe weaknesses which restricttheir usefulness in especially critical photographic applications. Inparticular, use of the above techniques and methods results in a loss ofimagery detail in regions of a photographic image close to abruptdiscontinuities of lighting on the original scene. A fundamentaltheoretical weakness of the above-described image enhancement is thatthe image on the negative is low-pass spatially filtered in forming themask. Spatial filtering of the image on the negative is undesirablebecause the range of transmissivity values of the negative is generallyvery large and, therefore, the image cannot be processed in the mosteffective fashion by spatial filtering. More particularly, the problemis that spatial filtering adds together contributions from differentparts of the image. Therefore, in regions of the image near sharpdiscontinuities of lighting, the spatial ltering adds togethercontributions from very light and very dark areas of the negative, withthe result that the contributions from the dark areas are swamped out bythose from the light areas. Consequently, the image enhancement is poorin these regions, and imagery detail is often lost.

Another method which has been used for enhancing photographic imageswhich merits brief discussion is cornmonly known as dodging or shadingIn this method, a photographer prepares masks of varyingtransmissivities cut to the shape of the light areas of the negative,and places them between the negative and the positive that is beingexposed. The masks are moved (or dodged) during the exposure, so thattheir outlines do not occur as detail on the positive. The effect of themasks is to attenuate the light from the low-density areas of thenegative and thereby compress the range of the exposure values appliedto the positive. A general disadvantage of the dodging method is thatthe masks are prepared in accordance with the qualitative judgment ofthe photographer. Consequently, parts of the imagery detail on thenegative may be lost or obscured, or by imagery detail 4 may be confusedby undesirable artifacts resulting from use of the masks. Therefore, theeffectiveness of the dodging method has been quite limited in manyphotographic applications where clarity and correctness of detail arestrict requirements.

SUMMARY OF THE' INVENTION Briefly, the present invention relates to areiterative feedback image enhancement process which comprises aninitial cycle followed by at least one subsequent cycle and a finaloperation. In the initial cycle of the reiterative feedback imageenhancement process, an original image relating to a scene is producedfrom which a compressed image is derived, the values of the compressedimage being a fixed function of the corresponding values of the originalimage. A filtered image is then formed by low-pass spatially filteringthe compressed image. The initial cycle is completed by deriving a maskimage from the filtered image, the values of the mask image being afixed function of the corresponding values of the filtered image.

In each subsequent cycle of the reiterative feedback image enhancementprocess, a compressed image is derived from the original image and themask image derived in the preceding cycle, the values of the compressedimage being a fixed function of the product of the corresponding valuesof the original image and the mask image derived in the preceding cycle.A filtered image is then formed by low-pass spatially filtering thecompressed images derived in the present cycle and all previous cycles,the values of the filtered image being a weighted average of thecorresponding values of the low-pass spatially filtered compressedimages derived in the present and all previous cycles. The subsequentcycle is completed by deriving a mask image from the filtered imageformed in the preceding step, the values of the mask image being a fixedfunction of the corresponding values of the filtered image formed in thepreceding step.

To conclude the reiterative feedback image enhancement process, thefinal operation is performed which comprises the step of deriving anenhanced image from the original image and the mask image derived in thepreceding cycle, the values of the enhanced image being a fixed functionof the product of the corresponding values of the original image and themask image derived in the preceding cycle.

In the preceding brief description of the reiterative feedback imageenhancement process of the present invention, such terms as image, xedfunction, fixed function of the product, and weighted average have beenemployed. In order to more clearly understand and appreciate thespecific nature of the present invention, a brief discussion of theabove terms as to their meanings may be helpful.

The term image, in the context of the present invention, is intended tomean a two-dimensional array of data points having real values. An imagemay be conveyed in many ways, for example, on film as the transmissivityvalues of the exposed film. Alternatively, if the film is illuminated byeven illumination, the intensity values of the light emanating from thefilm may also represent an image the values of which are proportional tothe corresponding values of the image represented by the transmissivityvalues of the lm. As still another example, an image may be conveyed ona cathode ray tube as a two-dimensional array of brightness values.

To define the terms fixed function, fixed function of the product andweighted average, three images A, B, and C, each having a coordinatepoint (x, y) and a respective value Za, Zb, and Zd will be considered.Thus, in the context of the present invention, if a value of the image Bat the coordinate point (x, y) is a fixed function of a value of theimage A at the corresponding coordinate point (x, y), this means thatZ=y(Za), where 3(Z) is dependent only on the value ZB and is independentof any other variable including time and the coordinate point (x, y).Similarly, if a value of the image C at the coordinate point (x,y) is afixed function of the product of the values of the images A and B at theassociated coordinate points (x, y), this means that Z =f(Za-Zb), where1(ZaZb) is dependent only on the product (Za-Zh) and is independent ofany other variable including the individual Za and Zb values, time, orthe individual coordinate points (x, y). If a value of the image C atthe coordinate point (x, y) is a weighted average of the values of theimages A and B at the associated coordinate points (x, y), this meansthat Zc=K1Za+K2Zp, where K1 and K2 are constants.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 illustrates in a detailedschematic form the various steps employed in an exemplary three cyclesof the feedback image enhancement process of the present in- Vention;and

FIG. 2 is a schematic representation of apparatus ernployed to performlow-pass spatial filtering in accordance with the present invention.

DESCRIPTION OF A PREFERRED METHOD OF THE INVENTION Fundamental EquationsThe principal object of the present invention is to produce an imagewhich represents an enhanced version of an original negative image or anoriginal positive image of a scene. Although the principles and conceptsof the present invention apply equally well to the derivation of anenhanced negative image or to an enhanced positive image of a scene, thefollowing discussion will be directed to the more common and usualsituation in which a negative image of a scene, rather than a positiveimage of a scene, is derived, and from which an enhanced positive imageis produced.

In deriving an enhanced positive image, it is desired that the enhancedpositive image satisfy as closely as possible the following equation:

In Equation 1, Tp represents the relative transmissivity of the enhancedpositive at any point, B is the brightness of the corresponding point onthe scene that was photographed, Tp is the Value at the correspondingpoint of a low-pass spatially-filtered modification of the relativetransmissivity Tp, and K and Bo are constants. The relativetransmissivity Tp is defined as the ratio of the actual transmissivityof the enhanced positive to the maximum transmissivity of the unexposedfilm used to form the enhanced positive. In Equation 1, the parameter Kis termed an enhancement constant, and is a positive constant. In apreferred embodiment of the process of the invention, the enhancementconstant K has a Value typically about 1.5; the larger the value of theenhancement constant K, the greater is the compression of thephotographic data achieved by the feedback image enhancement process ofthe present invention. The parameter Bo in Equation 1 is a constantwhich pertains to the relative transmissivity Tp of the enhancedpositive. Preferably, the values of the constant B is chosen such thatthe average value of the relative transmissivity Tp over the enhancedpositive is approximately equal to 0.5. Theoretical and experimentalstudies have shown that high quality image enhancement is achieved ifEquation 1 is satisfied.

As indicated above, Tp represents a low-pass spatially filteredmodification of the relative transmissivity Tp. The spatial filteringoperation at a point having coordinates (x, y) can be described by theintegral equation where x and y are variables in the x, y coordinatesystem over which the integration is performed, r is the radial TD (x:y)

distance between the point (x, y) and a variable point (x', y'), and isgiven by r=\/(x-x')2l(y-y')2 (3) and WU) is a weighting function for thespatial filtering operation. The weighting function W(r) in Equation 2decreases with increasing values of r.

It may be noted that vEquation 1 expresses Tp as a function of Tp andEquation 2 expresses Tp as a function of Tp. These two equations cannotbe combined to Obtain an explicit relationship between the scenebrightness B and the relative transmissivity Tp of the enhancedpositive. Therefore, to solve these equations, the present inventionuses a reiterative, feedback process which converges to a steady-statesolution in which Equations l and 2 are both closely approximated. Inthis feedback process, successively closer approximations of the idealrelative transmissivity Tp are `formed in successive cycles of theprocess.

Equation 1 can also be expressed in the alternative forms To apply theserelations to photographic lfilms, it is necessary to consider thegeneral sensitometric properties of film. The density DN of a negativeis defined by Where TN is the absolute transmissivity of the negative.Over a large part of the operating range of most films, the logarithm ofthe transmissivity is approximately a linear function of the logarithmof the exposure. This region is called the linear range of the film.Hence, in the linear range, the density DN of the negative isapproximately a linear function of the logarithm of exposure EN, and socan be approximately expressed as DN'YN login EN-l-Cr (7) where yN andC1 are constants. The parameter ryN is called the gamma of the lm. Theexposure EN applied to the negative at any point is proportional to thebrightness B at the corresponding point in the scene. Hence, in thelinear range, the density DN of a point on the negative is relatedapproximately to the brightness B at the corresponding point in thescene by the expression where C2 is a constant. Substituting Equation 8into Equation 5 gives -where C3 is a constant. The approximation ofEquation 9 is considered the best approximation of Equation 5 that canbe achieved in a practical manner. Therefore, this approximation isregarded as being the desirable goal for the feed back image enhancementprocess of the present invention. Thus, the approximately equal sign inEquation 9 can be replaced by an equal signa and so the process of thepresent invention operates to satisfy as closely as possible theequation To implement Equation l0, a mask is prepared which is thensuperimposed on the original negative. The density Ds of themask-negative combination is given by DS=DN+DM (11) where DM is thedensity of the mask. In order to implement Equation 10 by means of themask, `Equation 10 is expressed in the forms and where do is a constant.Comparing Equations and 13 shows that the density of the mask DM may begiven by DML- 1.74KYNTp-I-dM where dM is a constant. As |was mentionedheretofore, the constant B0 in Equation 1 is preferably chosen so thatthe average value of the relative transmissivity Tp over the enhancedpositive is equal to approximately 0.5 Consistent therewith, theconstant do in Equation 13 is preferably chosen so that the averagevalue of the relative transmissivity Tp over the enhanced positive isequal to approximately 0.5.

Since the image enhancement process of the present invention operates ina feedback manner, it is necessary that damping be incorporated into theprocess in order for the reiteration to converge to a suitable solution.The damping is achieved by providing memory between successive cycles ofthe feedback process. This memory or damping is achieved by a dampingcomputation routine that combines information from successive cycles. Aneffective computation for achieving the damping is given by Theparameter K in Equation 15 is the previously mentioned enhancementconstant; x, and xo are input and output imagery variables,respectively, of the damping computation routines xo(q) and xo(q-1) areoutput variables for the (q) and (q-l) cycles, respectively, of thefeedback image enhancement process; and xi(q) is the input variable forthe (q) cycle. Equation 15 expresses the output variable x0 for onecycle (q) in terms of the output variable for the previous cycle (c1-1).If `Equation 15 is solved for the relationship between input and outputvariables, the following equation is derived ma) r-f (qq) (16) Equation16 shows that the output imagery variable :to for the dampingcomputation routine is a weighted average of the input imagery variablesfor the latest and all earlier cycles of the feedback image enhancementprocess. It can be shown from this equation that after several cycles,as the process approaches a steady state condition, xo is approximatelyequal to xi.

The damping computation briefly described above may be convenientlyperformed in terms of the low-pass spatially-filter variable Tp.Specifically, the variable Tp I nay be designated as the input imageryvariable xi, and Tp as the output imagery variable x0. Equations 13, 14,and 16 then become, respectively,

The expression Tp(ql1) of Equation 17 represents the transmissivity ofthe approximation to the enhanced positive (which may be called simplythe positive) for the (q-i-l) cycle. In the last cycle of the imageenhancement process, the possitive is taken to be the enhanced positivebecause it represents the closest approximation to the ideal enhancedpositive image.

Although Equations 17 through 19 are stated in terms of the imageryvariable "Tp, it is to be appreciated that the damping can |be performedin terms of other imagery variables. Such modifications, however, do notalter the basic concept of the invention.

Description of the feedback image enhancement process.-(FIG. 1

Referring to FIG. 1, there is shown in schematic form and in accordancewith a preferred embodiment of the present invention, the various stepsof the photographic feedback image enhancement process. As indicated byFIG. 1, the feedback image enhancement process comprises three cycles ofthree steps (a) through (c), and a final step, which are performed insequence with feedback being provided between the last step (step (c))in each cycle and the first step (step (a)) in the next succeedingcycle, as indicated by the dotted FEEDBACK arrows. Although three cyclesof steps (a)(c) are shown in FIG. 1, satisfactory photographic feedbackimage enhancement can often be achieved by only two cycles. The maximumnumber of cycles required to achieve a desired quality of imageenhancement is determined in accordance with the accuracy and precisionrequired in the particular application. Inasmuch as the output of thelast step of each cycle (excepting the last cycle) is used in the firststep of the next succeeding cycle, the desired output of the process,that is, the output of the final cycle (third cycle), is obtained as aresult of an iterative operation in which the output of each successivecycle represents a closer approximation to the ideal output. Theoperation of the feedback image enhancement process depicted in FIG. 1will now be described.

For simplicity, the photographic steps (a) and (c) of FIG. 1 are assumedto be implemented by contact printing. However, more complicated opticalimaging can be used. {[n the feedback image enhancement process to bedescribed, different types of films may be used in the three steps (a),(b), and (c), but the same film type is used in the corresponding stepsof the various cycles (e.g., step (b) of the third cycle uses the same-lm as steps (b) of the first and second cycles.)

First cycle-In step (a) of the first cycle, a negative transparency Nrecording a photographic image of a scene is uniformly illuminated toexpose a photographic film which is then developed to provide a firstpositive transparency P01). 'Ihe photographic film is operated in thenon-linear toe of its sensitometric curve, and so the range of imagerydata recorded on the negative N is compressed in this step. Hence, thefirst positive 13(1) records a compressed image. Additionally, thetransmissivity values at the points in the first positive P(1) are afixed function of the transmissivity values of the negative N at thecorresponding points. As will be explained more fully hereinafter, thegamma yp of the positive P(1) vfilm used in step (a) is preferably,though not necessarily, equal to the reciprocal of the gamma 'yN of thenegative N. The value of the illumination exposure is adjusted in thisstep so that the relative transmissivity Tp of the first positive P1(1)has an average value over the positive preferably equal to Tp=0.5,although this particular value need not be satisfied very accurately. Aswill be shown later, the above conditions cause the process toapproximately satisfy Equation 17 for many types of films. (Note thatfor the first cycle, the density of the mask DM(q) in Equation 17 iszero.)

In step (b), the Iirst positive PCI) is uniformly illuminated and theimage formed thereby is low-pass spatially filtered (i.e., blur1ed) bysuitable apparatus of a type such as shown in FIG. Z. Details of thelow-pass spatial filtering apparatus of FIG. 2 will later be presented.The blurred image is projected onto a. photographic film which is thendeveloped to provide a first blurred negative B(1). Preferably, thephotographic film in this step is one which has been previously slightlyexposed (or fogged) with a uniform illumination. The purpose of foggingthe film is to cause the film to operate in the desirable part of itssensitometric characteristic. More particularly, the fogging andillumination intensities are adjusted in the present step so that thefilm exposed by the illumination is operated in the range of itssensitometric curve where density is approximately alinear function ofexposure. This condition satisfies Equation 118 as will be explainedhereinafter.

In step (c), the first blurred negative B(1) is illuminated uniformly toexpose film which is then developed to provide a first mask M(1). Thetransmissivity values at the points in the first mask M(1) are a fixedfunction of the exposure Values of the first blurred negative B(1) atthe corresponding points. The value of the illumination exposure in thisstep is adjusted such that the film operates in the linear range of itssensitometric curve. Therefore, the density dM of the mask M(1) is alinear function of the density DB of the first blurred negative B(1),which in turn is a linear function of the exposure applied to the first`blurred negative B(1). Thus, the density DM of the mask is a linearfunction of the exposure applied to the blurret negative B(1), acondition which satisfies Equation li As indicated by the dotted FEEDBACarrow in FIG. 1, the first mask M(1) is then use d in step (a) of thesecond cycle of the process. The mask M(,1) contains a blurred positiveimage, and so is dar-k in the areas where the negative N is light, andvice versa. p

Second cycle-In step (a) of the second cycle, the first mask M(1) issuperimposed on the negative N, and the combination is uniformlyilluminated to expose a film which is then developed to provide a second(compressed) positive P(2). In this step, the transmissivity values atthe points in the second positive P(2) are a fixed function of theproduct of the transmissivity values at the corresponding points in thenegative N and the first mask M(1). As in the first cycle, the value ofthe illumination exposure is adjusted such that the average value overthe image of the relative transmissivity Tp of the second positive P(2)is equal to 0;-5. To achieve this value of T=0.5 requires greaterillumination than in the first cycle because of the attenuation providedby the mask M01) [n step (b), the first positive P(1) exposed in thefirst cycle and the second positive PU.) exposed in the present cycleare uniformly illuminated in sequence, and the projected images arelow-pass spatially filtered (by apparatus such as that of FIG. 2) anddirected onto film which has been previously fogged as in the firstcycle. The same amount of fogging is used in this step as in thecorresponding step of the first cycle. The film is then developed toprovide a second blurred negative B(2). It is to be noted that ifmultiple spatial filtering apparatus is provided in this step, thelow-pass spatially filtered positive images may be projectedsimultaneously onto the fogged film and in registration with each other,instead of in sequence as described above.

The amount of illumination exposure applied to each of the positivesP(1) and P(2) is determined in accordance with the damping computationroutine of Equation 16. For example, if the previously mentioned valueof K=l.5 is assumed, the factor (2K-1)/(21K+'l)` in Equation 16 is equalto 1/2. For this condition, the illumination exposure applied to aparticular positive is reduced by a factor of two for each succeedingcycle. In the present case, therefore, the first positive P(1) receivesone-half the illumination exposure received during the first cycle andthe second positive P(2) receives the same illumination exposure thatthe first positive P(1) was given during the first cycle. Thus, theaverage illumination values at the points in the second blurred negativeB(2) are a weighted average of the illumination values at thecorresponding points in the low-pass spatially filtered positive images.This point is discussed in more detail hereinafter. v

In step (c), the second blurred negative B(2) is uniformly illuminatedto expose film which is then developed to provide a second mask M(2).The transmissivity values at the points in the second mask M(2) are afixed function of the exposure values of the second blurred negativeB(Z) at the corresponding points. As in the previous cycle, theillumination exposure is adjusted such that the film used to form thesecond mask M(2) operates in the linear range of its sensitometriccurve. The second mask M(2) is then used in step (a) of the third andfinal cycle of the process.

Third cycle-In step (a) of the third cycle, the second mask M(2) issuperimposed on the negative N and the combination is uniformlyilluminated to expose a lm which is then developed to provide the third(compressed) positive 1)(3), In this step, the transmissivity values atthe points in the third positive P(3\) are a fixed function of theproduct of the transmissivity values at the corresponding points in thenegative N and the second mask M(2). As in previous cycles, the value ofillumination exposure is adjusted such that the average value of therelative transmissivity Tp of the third positive P(3\) is `0.5.

. In step (b), the positives P( 1), P(2), and P(3') are uniformlyilluminated in sequence, (or simultaneously), and the projected imagesare low-pass spatially filtered and directed onto lfilm which has beenpreviously fogged as in the previous cycles. The same amount of foggingis used as in the corresponding steps of the previous cycles. The filmis then developed to provide a third blurred negative B(3). For theassumed typical value of 16:15, the illumination exposure applied to thefirst positive P(1) is one-quarter the illumination exposure appliedthereto in the first cycle; the illumination exposure applied to thesecond positive P(2) is one-half that applied to the -rst positive P(.1)in the first cycle; and the illumination exposure applied to the thirdpositive 1)(3) is equal to the illumination exposure applied to thefirst positive P(1) in the first cycle. Thus, the average illuminationvalues at the points in the third blurred negative B(3) are a weightedaverage of the illumination values at the corresponding points in thelow-pass spatially filtered positive images.

. In step (c), the third blurred negative B(3) is uniformly illuminatedto expose 4film which is then developed to provide a third and finalmask M(3). The

' transmissivity values at the points in the third mask M(3) are a fixedfunction of the exposure values of the third blurred negative 13(3) atthe corresponding points. As in previous cycles, the illuminationexposure is adjusted such that the film used to form the third maskM(\3) operates in the linear range of its sensitometric curve.

Final step.-The process is concluded by superimposing the third maskM(3) on the starting negative N, and the combination is uniformlyilluminated to expose film or photographic printing paper which is thendeveloped to provide an enhanced positive EP. The enhanced positive EPis a print or transparency of any suitable form or size. In this step,the transmissivity values at the points in the enhance positive EP are afixed function of the product of the transmissivity values of thenegative N and the third mask M(3) at the corresponding points.

' In the above-described feedback image enhancement process, care isexercised to keep the image of the various steps appropriatelycontrolled in size and registration. A convenient approach is to use 1:1contact prints in steps (a) and (c), and to spatially filter in step (b)in such a manner that no change in size results. Appropriateregistration marks can be applied to the films to keep the images inproper registration. Further, it is to be appreciated that enlarging orreduction can be employed at any step of a cycle provided that the sizechange is compensated for by appropriate reduction or enlarging atanothery step. Y

1 1 IDetailed equations for feedback image enhancement process Thelogarithm of the exposure Ep applied to the positive,y

is proportional to the density Ds of the combination.

Hence, y

Ds=`-10g1o (C4Ep) (21) where C4 is a constant that depends on theillumination exposure applied to the mask-negative combination whenexposing the positive. From Equation 21, Equation 2O can be expressed inthe form where C6 is a constant. Equation 23 can also be expressedalternatively as i TD: i1-tanh loge (CEDl/Wni where C6 is a constant.Equation 24 can also Ibe expressed as Tv=[1+C'E/"Nl1 (24) Equation 24relates the exposure Ep applied to a positive in step (a) to therelative transmissivity Tp of the positive. Commercially-available filmoften closely approximates the following characteristic in thelow-exposure region:

T--[1|C7E^]1 (25) where T is the relative transmissivity of the exposedfilm, E is the exposure applied to the film, 'y is thel `gamma of thefilm, and C7 is a constant. Comparing Equations 24 and 25 shows that thedesired characteristic for step (a) can be very adequately satisfied bymany films where the gamma 'yp of the film used to derive the positiveis given by 'vp=(1N) (26) Thus, for step (a), a fihn is preferablyselected for the positive which has a gamma yp equal to the reciprocalof the gamma fyN of the original negative. As stated pre-- viously, theillumination exposure in step (a) is preferably selected such that theaverage relative transmissivity Tp of the positive over the whole imageis approximately equal to 0.5.

Step (b).-For simplicity in the ensuing discussion, the relativetransmissivities of the first, second, third, etc. positives (exposed inthe first, second, third, etc. cycles) may be conveniently designated asTp(1), Tp(2),

Tp(3), etc., respectively. The time integral of the inwhere TPU) is thelow-pass spatially-filtered kmodification of the image Tp(1). Equation27 assumes that there 1s no change of image size in the spatialfilteringFrom Equation 19, the exposure applied to the blurrednegativeduring the qth cycle is Thus from Equation 19Eb(q)=[Eb0(2Kl1)/2^]T'p(q) (29) Near the toe of the sensitometric curveof most lms there is a non-linear region where the density isapproximately a linear function of exposure. In some films, thisregioncovers a larger range than in others. In step (b), the film ispreferably operated in this nonlinear region by fogging the film to(establish a minimum value of exposure at the lower limits of thisregion), and by controlling the illumination (so that the maximumexposure does not exceed the upper limit of this region). Therefore, thedensity DB of the blurred negative B exposed in step (b) is related asfollows to the exposure Eb applied after fog- DB= [DB/EBTEB-l-Cs (30)where C3 is a constant and (BDB/EEB) is the slope of thedensity-versus-exposure curve in the non-linear region where the film isoperated. Substituting Equation 29 into Equation 30 gives E(2Kl1)][BB]Dfi: 2 eEB TD (si) Step (c).-The film for producing the mask M isoperated completely in its linear range, and so the density DM of themask M is given by DM='YM 10810 EM-i-Cs (32) where yM is the gamma ofthe mask film, EM is the exposure applied to the lm, land C9 is aconstant. The exposure EM applied to the mask film is proportional tothe transmissivity of the blurred negative. Hence, Equation 32 can beexpressed as where C10 is a constant. Substituting Equation 31 intoEquation 33 gives DM= ('1/2 iMEbo( 2K-l-1 (DB/EB) T1Jl-C11 (34) whereC11 is a constant. Equating Equations 18 and 34 gives E *[2(1.74)K:|2K+1 7M eDB 35) Equation 35 describes the illumination exposure requiredfor the lastest positive in step (b) to achieve a particular value oftheenhancement constant K.

A convenient means of setting Eho is to illuminate a clear positive withthe exposure Ebo for which the relative transmissivity TP is unity, andthereby expose a blurred negative B, and from this produce la mask M. Amask is also produced from a blurred negative B which is unexposedexcept for the fogging. The differences in the densities of these twomasks, designated as ADM' is equal to l ADM==7M[DB/EB]E11Q (36)Substituting Equation 36 into Equation 35 gives ADM-:3.48K'yN/(2K-I-1)(37) Low-pass spatial filtering apparatus-FIG. 2

In step (b) of each cycle of the feedback image enhancement process ofthe present invention, a spatial filtering operation is performedwherein the images off the various positives are filtered to attenuatethe high spatialfrequency components thereof. The spatial filtering maybe accomplished in several ways. For example, spatial filtering may beaccomplished in a somewhat crude manner by conventional photographicoptical apparatus by simply defocusing the optics of the apparatus. Theeffect of the defocusing is to blur each line of the image on thepositive into a uniform band in the defocused image. The cross sectionof a blurred line produced by such defocusing is a square. Therefore,the transfer function of the simple defocusing operation is the Fouriertransform of a -square pulse which is (sin AW) /AW, where W is afrequency variable and A is a constant. Since this transfer functionprovides attenuation of high-frequency data, the defocusing operationrepresents a low-pass spatial filtering operation. However, theabove-mentioned transfer function has an infinite series ofhigh-frequency peaks which gradually decay with increasing spatialfrequency. These peaks add undesirable high spatial-frequency detail tothe defocused image which cause artifacts to appear in the resultantenhanced image.

To achieve more effective spatial filtering, a line on the originalnegative image should produce a blurred image that peaks at the centerand decays gradually and monotonically from the center (approximatelylike an exponential function). This characteristic can be achieved bydesigning Ia projection lens so as to have appropriate abberationswhereby the blurred image peaks at the center and decays gradually andmonotonically from the center. Another approach is to defocus the opticsof a projection system, and to vary the aperture of a lens included inthe projection system during the exposure by means of an iris. As theaperture is increased, the width of the blurred line increases, and sothe average blurred line can be appropriately shaped.

A more suitable and convenient apparatus for providing effectivelow-pass spatial frequency filtering is shown at 20 in FIG. 2. As showntherein, the low-pass spatial frequency filtering apparatus 20 comprisesa diffuse radiator 21, such as a set of fluorescent lamps covered by afrosted glass, a spatial filter mask 22 spaced from the diffuse radiator21, and a lens 23 spaced from the spatial filter mask 22 by a distanceequal to the focal length of the lens 23. The spatial filter mask 22 isa transparency with a circularly-symmetric transmissivity pattern suchthat the transmissivity is maximum at the center of the mask anddecreases gradually from the center of the mask to the edge of the mask.

In operation, light rays are directed by the diffuse radiator 21 throughthe spatial filter mask 22. Because of the above-mentioned variabletransmissivity pattern of the spatial filter mask 22, a central lightray Re illuminating a particular point on the lens 23 has a greaterintensity than a side ray R1 or a side ray R2 passing through the mask22 at the outer edges thereof where the transmissivity is less than atthe center. The lens 23 refracts the incident light so that the centralray RC is parallel to the axis of the lens 23 and the side rays R1 andR2 remain slightly divergent. By the above action, a positive trans- 14parency is illuminated by somewhat diffused light in which theperpendicular rays have the maximum intensity and the intensitydecreases with angle from the perpendicular in accordance with thetransmissivity function of the spatial filter mask 22. Unexposed lrn isplaced an appropriate distance below the positive transparency to obtainthe desired width of the spatial blur. The shape of the blur on theblurred negative for each point in the enhanced positive depends uponthe transmissivity pattern of the spatial lter mask 22. When spatialfiltering is accomplished with the arrangement 20 of FIG. 2, the blurredimage of a line has a desirable cross-section that peaks in the centerand decays gradually at both sides of the center.

Modifications In the practical embodiment of the invention describedhereinbefore, the images in all the steps of the process are recordedphotographically. However, in other embodiments of the invention,different media may be used for storing the imagery data. Nevertheless,these variations of implementation do not alter the principle of theinvention.

For example, the function of the mask may be irnplemented by means of acathode ray tube, rather than by photographic film, as in the practicalembodiment described hereinbefore. The mask image is then represented bythe two-dimensional pattern of brightness over the surface of thecathode ray tube rather than by the two-dimensional pattern oftransmissivity values over the transparency that forms the mask in thepractical embodiment described hereinbefore.

As another alternative embodiment, the spatial filtering can beperformed electronically rather than optically. More particularly, thecompressed positive transparency is scanned to form an electronicsignal, and the signal is then processed electronically to form aspatially filtered imagery signal.

What is claimed is:

1. Spatial filtering apparatus comprising:

a source of diffused illumination;

a mask disposed in front of the source of diffused illumination andhaving a circularly-symmetric transmissivity pattern; and

a lens spaced in front of the mask a distance equal to the focal lengthof the lens for refracting illumination directed thereon from the sourceof illumination after passage through the mask.

References Cited UNITED STATES PATENTS JOHN K. CORBIN, Primary ExaminerU.S. Cl. XR.

